Every player has full physical access to all regions in the game (apart from the PvMP region). They can enter those regions, kill enemies and complete quests in the Epic questline.
As a free player you will initially only have access to quests and deeds in the free zones (Shire, Ered Luin, Bree-land, Lone-Lands). If you wish to complete quests and deeds in other zones you will need to purchase the associated quest pack or expansion (this can be done with points earned in game if you have the time to earn them).
When downloading the free version of this game, will I have access to the areas added in the expansions such as Moria.
Ozeagle is completely correct. It may help you to think of it this way: the software you downloaded contains everything. Everyone is using the same version of the software. However, you have access to whatever content you have unlocked. Some content is unlocked by doing quests. Some is unlocked by buying a quest pack or expansion in the Store. Some is unlocked by subscribing (becoming VIP).
And when I say "content", I mean quests and deeds. Every player can travel to every location (once they are high enough level or unlock it with quests). F2P players are definitely not second-class citizens.
Oddly, you can deed in Great River without owning the quest pack - as a new player you won't, because it's a level 75 area.
But I noticed it when I went up there to do the epic - got most of the explorer deeds done and credited and some of the slayer deeds started before I purchased the quest pack. It may be a bug, I really don't know.